When AA Gill, a television critic, wrote that Professor Mary Beard was barely an inch off becoming the freakish subject of a Channel 4 dating show, the critic was – as well as being outrageously rude for comic effect – referring to the way in which TV judges us by our looks.

His words, which caused understandable offence, were a specific dig at one documentary, The Undateables, on which people deemed wildly unattractive are paraded on screen, but it happens on lots of other popular shows. Unhappy subjects are told what to wear, to get their teeth fixed or sent out to sink or swim in the sexual marketplace.

Professor Beard, a Cambridge academic and a prolific blogger long before she became a TV presenter, is not in search of such advice. She has found a life and is happy with her look. In fact, as she confides on a recent blog posting, she actually did brush her hair quite frequently on location during the filming of her new BBC2 series, Meet the Romans.

So hers is not a deliberately unkempt style; it is a natural look shared by the majority of those you might pass on the pavements of a British city. It is certainly not the plastic, spooky appearance of many women who appear on television. In truth, these lovelies must provoke many more curious stares on the bus to the television studio.

Since Gill's remarks, Beard has been hailed across the media as a refreshing "anti-autocutie", although not every commentator has rushed so gallantly to her aid. Writing in London's Evening Standard, Anne McElvoy argued acidly that: "It is as odd to go on TV expecting people not to notice your appearance as it would be to have your hair blow-dried to appear on the radio" and suggested that Beard is a smidge too intellectually self-satisfied.

It is dangerous, it has been noted, to annoy a classicist. Nemesis, the Greek deity of retribution and indignation, was a winged goddess, after all, and swift in dispensing dues. Her particular ire, it seems, was reserved for those who enjoy inordinate good fortune and commit unkindnesses with impunity – say, for example, someone paid to review television shows.

Beard's influential blog A Don's Lifemakes great play of examining such commonplace classical allusions, whether they relate to Nick Clegg or the origins of the Olympics. She aims, like Gill, to be provocative, typically wondering publicly whether one of Zoffany's paintings at the current Royal Academy show depicts three condoms hanging from a shelf. She also spends time online explaining how the Romans were not really shorter than us and that Christians were not killed in the Colosseum, so it was always likely that her educational zeal would one day transfer to television.

The only child of a father who was an "old-fashioned liberal architect" and a headmistress mother, the family home was in Much Wenlock, Shropshire.

Beard attended a private girls' school, Shrewsbury High, and was inspired by trips to the British Museum. "I was really good at Latin at school, and because I was good at it I got more interested and got better at it. When I was 12, it was very satisfying to be in control," she has recalled. At 18, she made her first trip to Pompeii and was troubled by mismatches with what she had been taught.

As a student at Newnham College, Cambridge, her walls bore images of the black American feminist pioneer Angela Davis. In 1984, she returned to the college, only a little mellowed, as the only female classics lecturer at the university. Writing the first in a series of successful books about Romans, she married Robin Cormack in 1985, had two children and became classics editor of the Times Literary Supplement in the early 1990s.

Last year, Beard's crusading attitude to her subject saw her teaching in Jamie Oliver's Dream School on television. "She's pulled off that rare trick of becoming a don with a high media profile who hasn't sold out, who is absolutely respected by the academy for her scholarship," assesses Charlotte Higgins, author of books on classics themes and Guardian journalist. "She works like a Trojan, if you'll forgive the pun, and fearlessly or foolishly says yes to a lot of things – like teaching Latin on Jamie Oliver's programme – because of a sense of responsibility to the cause of classics that goes far beyond attending to her own academic reputation."

Her "earthy, essentially anti-authoritarian manner" is the same on and off screen, adds Higgins, who celebrates Beard's unpredictability. A self-confessed member of the awkward squad, the professor is not interested in the party line. "She doesn't do the obvious thing. She blindsides you," says Higgins. "It's both her great quality and her curse that she speaks her mind: she can get herself into a lot of unnecessary trouble, but what she says is always powerful and interesting."

Beard's most controversial comments to date followed the 9/11 attacks when she wrote in the London Review of Books: "However tactfully you dress it up, the United States had it coming. That is, of course, what many people openly or privately think." Her argument was far from a vicious gloat, she has claimed, and she merely wanted to point out that bullies "even if their heart is in the right place, will in the end pay the price". But Beard was vilified for her sentiments.

As likely to cadge a cigarette from a student as to ask them to conjugate a Greek verb, Beard is opposed to the elite image of her subject. "The importance of Mary is that she is the living embodiment of the fact that classics isn't just for posh people and men and in fact never has been. If we didn't have her, then the most public champion of classics would be Boris Johnson, which is all very well, of course, and good on him – but he's a mixed blessing," says Higgins.

Classics is "a very mature and self-aware analytical discipline that predates even theology in the history of the study of the humanities," says Tim Whitmarsh, professor of classics at Corpus Christi, Oxford. "It takes you out of your comfort zone to a pre-Judeo-Christian era." It also requires the study of history, philosophy and linguistics and so its reputation as the quality mark of the British ruling and diplomatic classes may not be entirely spurious.

Even before Meet the Romans was broadcast, Professor Beard was clever enough to predict that a few low insults might be coming her way. She has written of her feelings about her appearance: "I used to be scared of looking like this, but now I couldn't wish to be any different. Never mind the masochism of Botox. I can't even imagine dyeing my hair. It's not just the boring hours it would take. It's that every time you did it, you'd be reminded that you were hiding something. And how do you stop once you've started?"

It is certainly evident that caring about one's appearance can be equally unprofitable for an accomplished woman. Anna Ford recently talked poignantly of her lost youthful beauty, while both the home secretary, Theresa May, and Christine Lagarde, the French managing director of the International Monetary Fund, are scrutinised for every coiffed move they make.

Still happily married, Beard has no need to appear on a dating programme. McElvoy suggests the professor now seems rather like a high-handed Prospero offering to educate the beast Caliban, but to other ears the barbed banter between the professor and the television critic might resemble the exchanges of Shakespeare's reluctant lovers, Beatrice and Benedict. And as Cicero, one of Beard's heroes, said: "If we are not ashamed to think it, we should not be ashamed to say it."

Unfortunately, by acting the naughty schoolboy poking fun at the thought of sex with matron, the TV critic masked his more grown-up attack on Beard's scholarship. He accused her of projecting her own modern, liberal beliefs on to Roman life. For Tim Whitmarsh, this slur is just as unfounded as the gibe about Beard's looks.

"It is the academic's job to translate their subject material into an idiom that makes sense. It is crude to see that as modern reinvention. She is creating a dialogue that shows us how we are both like, and unlike, the Romans."